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\title{
  %Solving Linear and Nonlinear Partial Differential Equations
  %Using Domain Decomposition and Local Extreme Learning Machines
  Local Extreme Learning Machines and Domain
  Decomposition for Solving Linear and Nonlinear Partial Differential Equations
} 
\author{
  Suchuan Dong$^1$\thanks{Author of correspondence.
    Email: sdong@purdue.edu}, \ Zongwei Li$^2$
  \\
  $^1$Center for Computational and Applied Mathematics \\
  Department of Mathematics, 
  Purdue University \\
  West Lafayette, Indiana, USA \\
  $^2$Department of Mathematics,
  Purdue University\\
  Fort Wayne, Indiana, USA
 } 

\date{(December 4, 2020)}


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Keywords: {\em
  local extreme learning machine,
  extreme learning machine,
  neural network,
  least squares,
  nonlinear least squares,
  domain decomposition
}

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\section*{Acknowledgement}
This work was partially supported by
NSF (DMS-2012415, DMS-1522537). 

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